Never heard of Great Canyons - where exactly is that? Or do you by chance mean Kings Canyon?
On a visit to Yosemite a couple years ago we got very lucky with a bobcat that is very relaxed around people (we followed him for half an hour and I got a photo of him pausing with Half Dome in background). Workers in the village gallery say he is seen regularly, but of course there is no way to guarantee the timing (and no guarantee he is still alive, as he looked quite old). Other than that, however, Yosemite was a dud for wildlife and we were surprised to not see a single deer.
Kings Canyon and adjoining Sequoia has mule deer easily seen almost anywhere at dawn and dusk. Crescent Meadow (in Sequoia) is very reliable for black bear.